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Mathematics
Problem
Prove that the circles
x
2
+
y
2
+
2
a
x
+
2
b
y
=
0
x^2 + y^2 + 2ax + 2by = 0
x
2
+
y
2
+
2
a
x
+
2
b
y
=
0
and
x
2
+
y
2
+
2
a
1
x
+
2
b
1
y
=
0
x^2 + y^2 + 2a_1x + 2b_1y = 0
x
2
+
y
2
+
2
a
1
x
+
2
b
1
y
=
0
touch each other, if
a
b
1
=
a
1
b
ab_1 = a_1b
a
b
1
=
a
1
b
.
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